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<div class="title">SuiteSparseQRSupport.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2012 Desire Nuentsa &lt;desire.nuentsa_wakam@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2014 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_SUITESPARSEQRSUPPORT_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_SUITESPARSEQRSUPPORT_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;  </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt; <span class="keyword">class </span>SPQR; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> SPQRType&gt; <span class="keyword">struct </span>SPQRMatrixQReturnType; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> SPQRType&gt; <span class="keyword">struct </span>SPQRMatrixQTransposeReturnType; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SPQRType, <span class="keyword">typename</span> Derived&gt; <span class="keyword">struct </span>SPQR_QProduct;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;  <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SPQRType&gt; <span class="keyword">struct </span>traits&lt;SPQRMatrixQReturnType&lt;SPQRType&gt; &gt;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    {</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;      <span class="keyword">typedef</span> <span class="keyword">typename</span> SPQRType::MatrixType ReturnType;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    };</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SPQRType&gt; <span class="keyword">struct </span>traits&lt;SPQRMatrixQTransposeReturnType&lt;SPQRType&gt; &gt;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;      <span class="keyword">typedef</span> <span class="keyword">typename</span> SPQRType::MatrixType ReturnType;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    };</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SPQRType, <span class="keyword">typename</span> Derived&gt; <span class="keyword">struct </span>traits&lt;SPQR_QProduct&lt;SPQRType, Derived&gt; &gt;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    {</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;      <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    };</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  } <span class="comment">// End namespace internal</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html">   62</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1SPQR.html">SPQR</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SparseSolverBase.html">SparseSolverBase</a>&lt;SPQR&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;{</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseSolverBase.html">SparseSolverBase&lt;SPQR&lt;MatrixType_&gt;</a> &gt; <a class="code" href="classEigen_1_1SparseSolverBase.html">Base</a>;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType_::Scalar Scalar;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType_::RealScalar RealScalar;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keyword">typedef</span> SuiteSparse_long StorageIndex ;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix&lt;Scalar, ColMajor, StorageIndex&gt;</a> <a class="code" href="classEigen_1_1SparseMatrix.html">MatrixType</a>;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Map.html">Map&lt;PermutationMatrix&lt;Dynamic, Dynamic, StorageIndex&gt;</a> &gt; <a class="code" href="classEigen_1_1Map.html">PermutationType</a>;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;      ColsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>,</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;      MaxColsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    };</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <a class="code" href="classEigen_1_1SPQR.html">SPQR</a>() </div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;      : m_analysisIsOk(<span class="keyword">false</span>),</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        m_factorizationIsOk(<span class="keyword">false</span>),</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        m_isRUpToDate(<span class="keyword">false</span>),</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        m_ordering(SPQR_ORDERING_DEFAULT),</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        m_allow_tol(SPQR_DEFAULT_TOL),</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        m_tolerance (<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::epsilon</a>()),</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        m_cR(0),</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;        m_E(0),</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        m_H(0),</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        m_HPinv(0),</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        m_HTau(0),</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        m_useDefaultThreshold(<span class="keyword">true</span>)</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    { </div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;      cholmod_l_start(&amp;m_cc);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    }</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1SPQR.html">SPQR</a>(<span class="keyword">const</span> MatrixType_&amp; matrix)</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;      : m_analysisIsOk(<span class="keyword">false</span>),</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        m_factorizationIsOk(<span class="keyword">false</span>),</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        m_isRUpToDate(<span class="keyword">false</span>),</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        m_ordering(SPQR_ORDERING_DEFAULT),</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        m_allow_tol(SPQR_DEFAULT_TOL),</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        m_tolerance (<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::epsilon</a>()),</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        m_cR(0),</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        m_E(0),</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        m_H(0),</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        m_HPinv(0),</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        m_HTau(0),</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        m_useDefaultThreshold(<span class="keyword">true</span>)</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    {</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;      cholmod_l_start(&amp;m_cc);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;      compute(matrix);</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    }</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    </div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    ~<a class="code" href="classEigen_1_1SPQR.html">SPQR</a>()</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    {</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;      SPQR_free();</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;      cholmod_l_finish(&amp;m_cc);</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    }</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keywordtype">void</span> SPQR_free()</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    {</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;      cholmod_l_free_sparse(&amp;m_H, &amp;m_cc);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;      cholmod_l_free_sparse(&amp;m_cR, &amp;m_cc);</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;      cholmod_l_free_dense(&amp;m_HTau, &amp;m_cc);</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;      std::free(m_E);</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;      std::free(m_HPinv);</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    }</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160; </div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="keywordtype">void</span> compute(<span class="keyword">const</span> MatrixType_&amp; matrix)</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    {</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;      <span class="keywordflow">if</span>(m_isInitialized) SPQR_free();</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160; </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;      <a class="code" href="classEigen_1_1SparseMatrix.html">MatrixType</a> mat(matrix);</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;      </div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;      <span class="comment">/* Compute the default threshold as in MatLab, see:</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">       * Tim Davis, &quot;Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment">       * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 </span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment">       */</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;      RealScalar pivotThreshold = m_tolerance;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;      <span class="keywordflow">if</span>(m_useDefaultThreshold) </div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;      {</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        RealScalar max2Norm = 0.0;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; mat.<a class="code" href="classEigen_1_1SparseMatrix.html#a36b8cc95234b4e2de38a199b6b2af9fc">cols</a>(); j++) max2Norm = numext::maxi(max2Norm, mat.col(j).norm());</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;        <span class="keywordflow">if</span>(numext::is_exactly_zero(max2Norm))</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;          max2Norm = RealScalar(1);</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        pivotThreshold = 20 * (mat.<a class="code" href="classEigen_1_1SparseMatrix.html#a853a76dd42349fa2f3654a4a61e0f574">rows</a>() + mat.<a class="code" href="classEigen_1_1SparseMatrix.html#a36b8cc95234b4e2de38a199b6b2af9fc">cols</a>()) * max2Norm * <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;RealScalar&gt;::epsilon</a>();</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;      }</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;      cholmod_sparse A; </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;      A = <a class="code" href="namespaceEigen.html#a7794e77d4be556d1c965842e227bd572">viewAsCholmod</a>(mat);</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;      m_rows = matrix.rows();</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> col = matrix.cols();</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;      m_rank = SuiteSparseQR&lt;Scalar&gt;(m_ordering, pivotThreshold, col, &amp;A, </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;                             &amp;m_cR, &amp;m_E, &amp;m_H, &amp;m_HPinv, &amp;m_HTau, &amp;m_cc);</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;      <span class="keywordflow">if</span> (!m_cR)</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;      {</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">NumericalIssue</a>;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        m_isInitialized = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;      }</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;      m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;      m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;      m_isRUpToDate = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    }</div>
<div class="line"><a name="l00166"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#a64cda2ae789b922f8fd26681b651b1a3">  166</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1SPQR.html#a64cda2ae789b922f8fd26681b651b1a3">rows</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> m_rows; }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    </div>
<div class="line"><a name="l00171"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#ab64bb8ae0a003d572b1002779425d596">  171</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1SPQR.html#ab64bb8ae0a003d572b1002779425d596">cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cR-&gt;ncol; }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest&gt;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="keywordtype">void</span> _solve_impl(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a> &amp;b, <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Dest&gt;</a> &amp;dest)<span class="keyword"> const</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot; The QR factorization should be computed first, call compute()&quot;</span>);</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;      eigen_assert(b.<a class="code" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>()==1 &amp;&amp; <span class="stringliteral">&quot;This method is for vectors only&quot;</span>);</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;      <span class="comment">//Compute Q^T * b</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;      <span class="keyword">typename</span> Dest::PlainObject y, y2;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;      y = <a class="code" href="classEigen_1_1SPQR.html#af16584dd4a0bcd2e27f97d176c9ae517">matrixQ</a>().transpose() * b;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      </div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      <span class="comment">// Solves with the triangular matrix R</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rk = this-&gt;<a class="code" href="classEigen_1_1SPQR.html#a360b7ee252230b8983d12cb782d96936">rank</a>();</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      y2 = y;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;      y.resize((std::max)(<a class="code" href="classEigen_1_1SPQR.html#ab64bb8ae0a003d572b1002779425d596">cols</a>(),<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>(y.rows())),y.cols());</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;      y.topRows(rk) = this-&gt;<a class="code" href="classEigen_1_1SPQR.html#a7939887c48eeff55571f9810ebf86738">matrixR</a>().topLeftCorner(rk, rk).template triangularView&lt;Upper&gt;().solve(y2.topRows(rk));</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160; </div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      <span class="comment">// Apply the column permutation </span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;      <span class="comment">// colsPermutation() performs a copy of the permutation,</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;      <span class="comment">// so let&#39;s apply it manually:</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; rk; ++i) dest.row(m_E[i]) = y.row(i);</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = rk; i &lt; <a class="code" href="classEigen_1_1SPQR.html#ab64bb8ae0a003d572b1002779425d596">cols</a>(); ++i) dest.row(m_E[i]).<a class="code" href="classEigen_1_1DenseBase.html#af230a143de50695d2d1fae93db7e4dcb">setZero</a>();</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;      </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="comment">//       y.bottomRows(y.rows()-rk).setZero();</span></div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="comment">//       dest = colsPermutation() * y.topRows(cols());</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;      </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;      m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    }</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    </div>
<div class="line"><a name="l00203"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#a7939887c48eeff55571f9810ebf86738">  203</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1SparseMatrix.html">MatrixType</a> <a class="code" href="classEigen_1_1SPQR.html#a7939887c48eeff55571f9810ebf86738">matrixR</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot; The QR factorization should be computed first, call compute()&quot;</span>);</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;      <span class="keywordflow">if</span>(!m_isRUpToDate) {</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;        m_R = viewAsEigen&lt;Scalar,ColMajor, typename MatrixType::StorageIndex&gt;(*m_cR);</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        m_isRUpToDate = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;      }</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;      <span class="keywordflow">return</span> m_R;</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    }</div>
<div class="line"><a name="l00213"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#af16584dd4a0bcd2e27f97d176c9ae517">  213</a></span>&#160;    SPQRMatrixQReturnType&lt;SPQR&gt; <a class="code" href="classEigen_1_1SPQR.html#af16584dd4a0bcd2e27f97d176c9ae517">matrixQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;      <span class="keywordflow">return</span> SPQRMatrixQReturnType&lt;SPQR&gt;(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    }</div>
<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#af7a3ad7b3fa2814354159acea9e76d53">  218</a></span>&#160;    <a class="code" href="classEigen_1_1Map.html">PermutationType</a> <a class="code" href="classEigen_1_1SPQR.html#af7a3ad7b3fa2814354159acea9e76d53">colsPermutation</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;<span class="keyword">    </span>{ </div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;Decomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Map.html">PermutationType</a>(m_E, m_cR-&gt;ncol);</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    }</div>
<div class="line"><a name="l00227"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#a360b7ee252230b8983d12cb782d96936">  227</a></span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1SPQR.html#a360b7ee252230b8983d12cb782d96936">rank</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;Decomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;      <span class="keywordflow">return</span> m_cc.SPQR_istat[4];</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    }</div>
<div class="line"><a name="l00233"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#afab6d54d18da2ab683618846ec832472">  233</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SPQR.html#afab6d54d18da2ab683618846ec832472">setSPQROrdering</a>(<span class="keywordtype">int</span> ord) { m_ordering = ord;}</div>
<div class="line"><a name="l00235"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#a181fd76d24fc9c246c3ac7ad2c054b68">  235</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SPQR.html#a181fd76d24fc9c246c3ac7ad2c054b68">setPivotThreshold</a>(<span class="keyword">const</span> RealScalar&amp; tol)</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    {</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;      m_useDefaultThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;      m_tolerance = tol;</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    }</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    </div>
<div class="line"><a name="l00242"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#a4be65f22eebe8089910ab02205146ec6">  242</a></span>&#160;    cholmod_common *<a class="code" href="classEigen_1_1SPQR.html#a4be65f22eebe8089910ab02205146ec6">cholmodCommon</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> &amp;m_cc; }</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    </div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    </div>
<div class="line"><a name="l00250"></a><span class="lineno"><a class="line" href="classEigen_1_1SPQR.html#a5d11571b3eba295bd74512147fc52ba3">  250</a></span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code" href="classEigen_1_1SPQR.html#a5d11571b3eba295bd74512147fc52ba3">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;Decomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;      <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    }</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    <span class="keywordtype">bool</span> m_analysisIsOk;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;    <span class="keywordtype">bool</span> m_factorizationIsOk;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    <span class="keyword">mutable</span> <span class="keywordtype">bool</span> m_isRUpToDate;</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    <span class="keyword">mutable</span> <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    <span class="keywordtype">int</span> m_ordering; <span class="comment">// Ordering method to use, see SPQR&#39;s manual</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    <span class="keywordtype">int</span> m_allow_tol; <span class="comment">// Allow to use some tolerance during numerical factorization.</span></div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    RealScalar m_tolerance; <span class="comment">// treat columns with 2-norm below this tolerance as zero</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    <span class="keyword">mutable</span> cholmod_sparse *m_cR = <span class="keyword">nullptr</span>; <span class="comment">// The sparse R factor in cholmod format</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    <span class="keyword">mutable</span> MatrixType m_R; <span class="comment">// The sparse matrix R in Eigen format</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    <span class="keyword">mutable</span> StorageIndex *m_E = <span class="keyword">nullptr</span>; <span class="comment">// The permutation applied to columns</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    <span class="keyword">mutable</span> cholmod_sparse *m_H = <span class="keyword">nullptr</span>;  <span class="comment">//The householder vectors</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    <span class="keyword">mutable</span> StorageIndex *m_HPinv = <span class="keyword">nullptr</span>; <span class="comment">// The row permutation of H</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    <span class="keyword">mutable</span> cholmod_dense *m_HTau = <span class="keyword">nullptr</span>; <span class="comment">// The Householder coefficients</span></div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    <span class="keyword">mutable</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m_rank; <span class="comment">// The rank of the matrix</span></div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    <span class="keyword">mutable</span> cholmod_common m_cc; <span class="comment">// Workspace and parameters</span></div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    <span class="keywordtype">bool</span> m_useDefaultThreshold;     <span class="comment">// Use default threshold</span></div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m_rows;</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ,<span class="keyword">typename</span> &gt; <span class="keyword">friend</span> <span class="keyword">struct </span>SPQR_QProduct;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;};</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> SPQRType, <span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;<span class="keyword">struct </span>SPQR_QProduct : ReturnByValue&lt;SPQR_QProduct&lt;SPQRType,Derived&gt; &gt;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;{</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SPQRType::Scalar Scalar;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SPQRType::StorageIndex StorageIndex;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  <span class="comment">//Define the constructor to get reference to argument types</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  SPQR_QProduct(<span class="keyword">const</span> SPQRType&amp; spqr, <span class="keyword">const</span> Derived&amp; other, <span class="keywordtype">bool</span> transpose) : m_spqr(spqr),m_other(other),m_transpose(transpose) {}</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  </div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_transpose ? m_spqr.rows() : m_spqr.cols(); }</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_other.cols(); }</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  <span class="comment">// Assign to a vector</span></div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResType&gt;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  <span class="keywordtype">void</span> evalTo(ResType&amp; res)<span class="keyword"> const</span></div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    cholmod_dense y_cd;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    cholmod_dense *x_cd; </div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <span class="keywordtype">int</span> method = m_transpose ? SPQR_QTX : SPQR_QX; </div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    cholmod_common *cc = m_spqr.cholmodCommon();</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    y_cd = <a class="code" href="namespaceEigen.html#a7794e77d4be556d1c965842e227bd572">viewAsCholmod</a>(m_other.const_cast_derived());</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    x_cd = SuiteSparseQR_qmult&lt;Scalar&gt;(method, m_spqr.m_H, m_spqr.m_HTau, m_spqr.m_HPinv, &amp;y_cd, cc);</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;    res = <a class="code" href="classEigen_1_1PlainObjectBase.html#aaf9fcc07dc13f89cf71d4a4e2b220d24">Matrix&lt;Scalar,ResType::RowsAtCompileTime,ResType::ColsAtCompileTime&gt;::Map</a>(<span class="keyword">reinterpret_cast&lt;</span>Scalar*<span class="keyword">&gt;</span>(x_cd-&gt;x), x_cd-&gt;nrow, x_cd-&gt;ncol);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    cholmod_l_free_dense(&amp;x_cd, cc);</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  }</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  <span class="keyword">const</span> SPQRType&amp; m_spqr; </div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  <span class="keyword">const</span> Derived&amp; m_other; </div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  <span class="keywordtype">bool</span> m_transpose; </div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  </div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;};</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SPQRType&gt;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;<span class="keyword">struct </span>SPQRMatrixQReturnType{</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;  </div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  SPQRMatrixQReturnType(<span class="keyword">const</span> SPQRType&amp; spqr) : m_spqr(spqr) {}</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  SPQR_QProduct&lt;SPQRType, Derived&gt; <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator*</a>(<span class="keyword">const</span> MatrixBase&lt;Derived&gt;&amp; other)</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  {</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="keywordflow">return</span> SPQR_QProduct&lt;SPQRType,Derived&gt;(m_spqr,other.derived(),<span class="keyword">false</span>);</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  }</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  SPQRMatrixQTransposeReturnType&lt;SPQRType&gt; adjoint()<span class="keyword"> const</span></div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    <span class="keywordflow">return</span> SPQRMatrixQTransposeReturnType&lt;SPQRType&gt;(m_spqr);</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  }</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  <span class="comment">// To use for operations with the transpose of Q</span></div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  SPQRMatrixQTransposeReturnType&lt;SPQRType&gt; transpose()<span class="keyword"> const</span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    <span class="keywordflow">return</span> SPQRMatrixQTransposeReturnType&lt;SPQRType&gt;(m_spqr);</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  }</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  <span class="keyword">const</span> SPQRType&amp; m_spqr;</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;};</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160; </div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SPQRType&gt;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;<span class="keyword">struct </span>SPQRMatrixQTransposeReturnType{</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;  SPQRMatrixQTransposeReturnType(<span class="keyword">const</span> SPQRType&amp; spqr) : m_spqr(spqr) {}</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  SPQR_QProduct&lt;SPQRType,Derived&gt; <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator*</a>(<span class="keyword">const</span> MatrixBase&lt;Derived&gt;&amp; other)</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  {</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;    <span class="keywordflow">return</span> SPQR_QProduct&lt;SPQRType,Derived&gt;(m_spqr,other.derived(), <span class="keyword">true</span>);</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  }</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  <span class="keyword">const</span> SPQRType&amp; m_spqr;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;};</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160; </div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;}<span class="comment">// End namespace Eigen</span></div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_af230a143de50695d2d1fae93db7e4dcb"><div class="ttname"><a href="classEigen_1_1DenseBase.html#af230a143de50695d2d1fae93db7e4dcb">Eigen::DenseBase::setZero</a></div><div class="ttdeci">Derived &amp; setZero()</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:548</div></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_a2d768a9877f5f69f49432d447b552bfe"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a2d768a9877f5f69f49432d447b552bfe">Eigen::DenseCoeffsBase&lt; Derived, DirectWriteAccessors &gt;::cols</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1Map_html"><div class="ttname"><a href="classEigen_1_1Map.html">Eigen::Map</a></div><div class="ttdoc">A matrix or vector expression mapping an existing array of data.</div><div class="ttdef"><b>Definition:</b> Map.h:98</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_aaf9fcc07dc13f89cf71d4a4e2b220d24"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#aaf9fcc07dc13f89cf71d4a4e2b220d24">Eigen::PlainObjectBase&lt; Matrix&lt; Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ &gt; &gt;::Map</a></div><div class="ttdeci">static ConstMapType Map(const Scalar *data)</div><div class="ttdef"><b>Definition:</b> PlainObjectBase.h:642</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html"><div class="ttname"><a href="classEigen_1_1SPQR.html">Eigen::SPQR</a></div><div class="ttdoc">Sparse QR factorization based on SuiteSparseQR library.</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:63</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_a181fd76d24fc9c246c3ac7ad2c054b68"><div class="ttname"><a href="classEigen_1_1SPQR.html#a181fd76d24fc9c246c3ac7ad2c054b68">Eigen::SPQR::setPivotThreshold</a></div><div class="ttdeci">void setPivotThreshold(const RealScalar &amp;tol)</div><div class="ttdoc">Set the tolerance tol to treat columns with 2-norm &lt; =tol as zero.</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:235</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_a360b7ee252230b8983d12cb782d96936"><div class="ttname"><a href="classEigen_1_1SPQR.html#a360b7ee252230b8983d12cb782d96936">Eigen::SPQR::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:227</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_a4be65f22eebe8089910ab02205146ec6"><div class="ttname"><a href="classEigen_1_1SPQR.html#a4be65f22eebe8089910ab02205146ec6">Eigen::SPQR::cholmodCommon</a></div><div class="ttdeci">cholmod_common * cholmodCommon() const</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:242</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_a5d11571b3eba295bd74512147fc52ba3"><div class="ttname"><a href="classEigen_1_1SPQR.html#a5d11571b3eba295bd74512147fc52ba3">Eigen::SPQR::info</a></div><div class="ttdeci">ComputationInfo info() const</div><div class="ttdoc">Reports whether previous computation was successful.</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:250</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_a64cda2ae789b922f8fd26681b651b1a3"><div class="ttname"><a href="classEigen_1_1SPQR.html#a64cda2ae789b922f8fd26681b651b1a3">Eigen::SPQR::rows</a></div><div class="ttdeci">Index rows() const</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:166</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_a7939887c48eeff55571f9810ebf86738"><div class="ttname"><a href="classEigen_1_1SPQR.html#a7939887c48eeff55571f9810ebf86738">Eigen::SPQR::matrixR</a></div><div class="ttdeci">const MatrixType matrixR() const</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:203</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_ab64bb8ae0a003d572b1002779425d596"><div class="ttname"><a href="classEigen_1_1SPQR.html#ab64bb8ae0a003d572b1002779425d596">Eigen::SPQR::cols</a></div><div class="ttdeci">Index cols() const</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:171</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_af16584dd4a0bcd2e27f97d176c9ae517"><div class="ttname"><a href="classEigen_1_1SPQR.html#af16584dd4a0bcd2e27f97d176c9ae517">Eigen::SPQR::matrixQ</a></div><div class="ttdeci">SPQRMatrixQReturnType&lt; SPQR &gt; matrixQ() const</div><div class="ttdoc">Get an expression of the matrix Q.</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:213</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_af7a3ad7b3fa2814354159acea9e76d53"><div class="ttname"><a href="classEigen_1_1SPQR.html#af7a3ad7b3fa2814354159acea9e76d53">Eigen::SPQR::colsPermutation</a></div><div class="ttdeci">PermutationType colsPermutation() const</div><div class="ttdoc">Get the permutation that was applied to columns of A.</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:218</div></div>
<div class="ttc" id="aclassEigen_1_1SPQR_html_afab6d54d18da2ab683618846ec832472"><div class="ttname"><a href="classEigen_1_1SPQR.html#afab6d54d18da2ab683618846ec832472">Eigen::SPQR::setSPQROrdering</a></div><div class="ttdeci">void setSPQROrdering(int ord)</div><div class="ttdoc">Set the fill-reducing ordering method to be used.</div><div class="ttdef"><b>Definition:</b> SuiteSparseQRSupport.h:233</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html">Eigen::SparseMatrix&lt; Scalar, ColMajor, StorageIndex &gt;</a></div></div>
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<div class="ttc" id="aclassEigen_1_1SparseMatrix_html_a853a76dd42349fa2f3654a4a61e0f574"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#a853a76dd42349fa2f3654a4a61e0f574">Eigen::SparseMatrix::rows</a></div><div class="ttdeci">Index rows() const</div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:140</div></div>
<div class="ttc" id="aclassEigen_1_1SparseSolverBase_html"><div class="ttname"><a href="classEigen_1_1SparseSolverBase.html">Eigen::SparseSolverBase</a></div><div class="ttdoc">A base class for sparse solvers.</div><div class="ttdef"><b>Definition:</b> SparseSolverBase.h:70</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:442</div></div>
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<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_a7794e77d4be556d1c965842e227bd572"><div class="ttname"><a href="namespaceEigen.html#a7794e77d4be556d1c965842e227bd572">Eigen::viewAsCholmod</a></div><div class="ttdeci">cholmod_sparse viewAsCholmod(Ref&lt; SparseMatrix&lt; Scalar_, Options_, StorageIndex_ &gt; &gt; mat)</div><div class="ttdef"><b>Definition:</b> CholmodSupport.h:60</div></div>
<div class="ttc" id="anamespaceEigen_html_a9723b3ff0f2c99fe1081e3eb14380d4c"><div class="ttname"><a href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">Eigen::operator*</a></div><div class="ttdeci">const Product&lt; MatrixDerived, PermutationDerived, AliasFreeProduct &gt; operator*(const MatrixBase&lt; MatrixDerived &gt; &amp;matrix, const PermutationBase&lt; PermutationDerived &gt; &amp;permutation)</div><div class="ttdef"><b>Definition:</b> PermutationMatrix.h:517</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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